This preview shows page 1. Sign up to view the full content.
Unformatted text preview: e general expression for Qn can be analogously
derived from equation 2 by incorporating all of the headloss (13)
This can be further simplified by dividing through by Qn
to yield:
. (14) The CWCn term can be defined more explicitly by substituting the right sides of equations 8 and 10 for the A and B
terms in equation 14, resulting in .(15) The value of CWCn can be specified directly by the user
(if LOSSTYPE is specified as “SPECIFYcwc” in dataset 2b),
otherwise it will be calculated automatically by the model
using equation 15 (for cases when LOSSTYPE is specified as
“THIEM,” “SKIN,” or “GENERAL” in dataset 2b).
The nature of the linear wellloss term indicates that, if the
well is less than fully penetrating, the linear wellloss coefficient (B) would change inversely proportional to the fraction
of penetration (α =
), and the celltowell conductance
would be reduced accordingly. Also note that in an unconfined
(convertible) cell, MODFLOW assumes that the saturated thickness changes as the water table rises or falls. Therefore, when
the head changes in an unconfined cell containing a multinode
well, the value of CWCn must be updated by solving equation
15 again because both b and bw will have changed. Calculation of Water Level and Flow in the
MultiNode Well
The basic numerical solution process is described by
Bennett and others (1982), Halford and Hanson (2002), and
Neville and Tonkin (2004). It consists of an iterative process
with three basic steps:
1. solve the system of finitedifference equations for heads at
each node of the grid, Conceptual Model and Numerical Implementation
2. solve for the composite head (water level) in the well,
hWELL, and 3. solve for the flow rate at each node (Qn) and the net discharge from the well (Qnet). Specifying the Location of MultiNode Wells The net flow to a multinode well is simulated by summing the flow component to each node (Bennett and others,
1982; Fanchi and others, 1987; Halford and Hanson, 2002),
which is defined by equation 12 and the common head in each
node of the well. After the terms are collected and rearranged,
the net flow rate between a multinode well and the groundwater system is
, 7 (16) where m is the total number of nodes in a multinode well,
and Qnet is the net flow between the well and the groundwater
system (L3/T) and is equivalent to the flow at the wellhead
(negative in sign for a discharge or withdrawal well). Because
hWELL is common to all nodes in a multinode well, equation
16 can be rewritten as
(17)
The value of hWELL is not known explicitly but is needed
to estimate the flow rate between each well node and connected grid cell for a given multinode well and to test that the
drawdown does not exceed userspecified limits. Rearranging
equation 17 gives the head in the well (Halford and Hanson,
2002): (18) In solving the governing groundwater flow equation,
estimates of hWELL and Qn lag an iteration behind estimates
of hn because equations 17 and 18 are solved explicitly
assuming that hn is known. Halford and Hanson (2002)
note that this causes slow convergence of the solver if the
MNW cells are represented in MODFLOW as a generalhead
boundary (see McDonald and Harbaugh, 1988). Convergence
is accelerated by alternately incorporating the MNW cells
as specifiedflux boundary conditions in odd iterations and
as generalhead boundaries in even iterations. That is, while
solving the governing flow equation numerically, during odd
numbered iterations the values of Qn and Qnet are specified
from the latest known values and the head in the well is calculated using equation 18, and during even numbered iterations the head in the well is specified from the most recent
known value and the values of Qn and Qnet are calculated
using equations 12 and 17. In MODFLOW, a multinode well must be linked to
one or more nodes of the grid. The user has two options to
accomplish this through the input datasets. One does not have
to apply the same option to all wells.
In the first approach, the user can specify the number
of nodes of the grid that a particular well is associated with
(by specifying the value of NNODES in dataset 2a). Then the
layerrowcolumn location of each node (or cell) of the grid
that is open to the multinode well must be listed sequentially
in dataset 2d. The order of the sequence must be from the first
node that is located closest to the land surface or wellhead to
the last node that is furthest from the wellhead. This ordering is required so that the model can properly route flow [and
solute if the groundwater transport (GWT) process is active]
through the borehole. There are no restrictions on locations of
nodes, other than they be located in the active part of the grid.
Thus, wells of any geometry—whether vertical, slanted, or
horizontal—can be defined.
The second approach is only applicable for vertical wells.
It eliminates the need for the user to convert field data on
depths or elevations of open intervals to corresponding layers of the grid. With this approach, the...
View
Full
Document
 Winter '14

Click to edit the document details